I doubt it. Yugiri Mistwalker is more of a Doman name, one she probably took up to help hide what she actually was under her hood and mask.
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I doubt it as well, but at the same time presumably the Au Ra are also from Doma, or at least the ones we're playing. So it wouldn't surprise me too much.
I'd also doubt that Yugiri strictly ties into general Au Ra names, for reasons others already covered. I'm also willing to wager that there probably won't be any apostrophes involved like the miqo'te have. I've noticed a lot of people writing it as "Au'ra" when it's not, it was shown as two separate words "Au Ra", no apostrophe.
I suppose a purely plausible explanation would be that Yugiri was simply raised by Hyur's and that's why she has the name she does. I only brought her up because she's the only one we know of so far, and most NPC's seem to use the same naming convention of their race in general.
I suppose it's also possible she's using a fake name, but that seems less plausible.